Exam 15: Chi-Square Tests

Instruction 15-5 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Instruction 15-5,what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using α = 0.10?

Instruction 15-11 Recent studies have found that Australian children are more obese than in the past.The amount of time children spent watching television has received much of the blame.A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television.You are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance. | TV Hours | Weights 0-3 3-6 6+ Total More than 10 kg overweight 1 9 20 30 Within 10 of normal weight 20 15 15 50 More than 10 underweight 10 5 5 20 Total 31 29 40 100 -Referring to Instruction 15-11,how many children in the survey spend more than 6 hours watching TV and are more than 10 kg overweight?

Instruction 15-14 Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. Hong Kong New York Paris Yes 86\% 65\% 78\% No 14\% 24\% 22\% At the 0.05 level of significance,you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. -Referring to Instruction 15-14,the critical value of the test is ________.

The chi-square test of independence requires that the number of expected frequency in each cell to be at least 1.

Instruction 15-8 Four surgical procedures currently are used to install pacemakers.If the patient does not need to return for follow-up surgery,the operation is called a "clear" operation.A heart centre wants to compare the proportion of clear operations for the four procedures,and collects the following numbers of patients from their own records: | Procedure | Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance. -Referring to Instruction 15-8,the overall or mean proportion of clear operations is ________.

Instruction 15-14 Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. Hong Kong New York Paris Yes 86\% 65\% 78\% No 14\% 24\% 22\% At the 0.05 level of significance,you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. -Referring to Instruction 15-14,the value of the test statistic is ________.

Instruction 15-2 Many companies use well-known celebrities as spokespersons in their TV advertisements.A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent.Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson.The gender of the spokesperson and whether or not the viewer could identify the product was recorded.The numbers in each category are given below. Male Celebrity Female Celebrity Identified product 41 61 Could not identify 109 89 -Referring to Instruction 15-2,at 5% level of significance,the conclusion is that

Instruction 15-12 According to an article in Marketing News,fewer cheques are being written at grocery store checkout stands than in the past.To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance,the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-12,there is sufficient evidence to conclude that the proportions between year 1 and year 2 are different at a 0.05 level of significance.

Instruction 15-12 According to an article in Marketing News,fewer cheques are being written at grocery store checkout stands than in the past.To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance,the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-12,the assumptions need to perform the tests are satisfied.

Instruction 15-12 According to an article in Marketing News,fewer cheques are being written at grocery store checkout stands than in the past.To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance,the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-12,what is the critical value?

Instruction 15-11 Recent studies have found that Australian children are more obese than in the past.The amount of time children spent watching television has received much of the blame.A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television.You are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance. | TV Hours | Weights 0-3 3-6 6+ Total More than 10 kg overweight 1 9 20 30 Within 10 of normal weight 20 15 15 50 More than 10 underweight 10 5 5 20 Total 31 29 40 100 -Referring to Instruction 15-11,which of the following statements is correct?

For a chi-square goodness-of-fit test,the denominator is

Instruction 15-9 The director of admissions at a local university is interested in investigating if admissions status (admitted,waiting list,denied admission)is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to run a chi-square test of independence with a level of significance of 0.01. -Referring to Instruction 15-9,the decision made suggests that admissions status at the university is independent of the type of community in which an applicant resides.

Instruction 15-9 The director of admissions at a local university is interested in investigating if admissions status (admitted,waiting list,denied admission)is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to run a chi-square test of independence with a level of significance of 0.01. -Referring to Instruction 15-9,the value of the test statistic is ________.

Instruction 15-12 According to an article in Marketing News,fewer cheques are being written at grocery store checkout stands than in the past.To determine whether there is a difference in the proportion of shoppers who pay by cheque among three consecutive years at a 0.05 level of significance,the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-12,what is the form of the null hypothesis?

Instruction 15-4 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced.The quality control department wants to find out whether there is a relationship between years of experience and defect rate.Since the job is repetitious,after the initial training period any improvement due to a learning effect might be offset by a loss of motivation.A defect rate is calculated for each worker in a yearly evaluation.The results for 100 workers are given in the table below. Years Since Training Period < Year 1 - 4 Years 5 - 9 Years High 6 9 9 Defect Rate: Average 9 19 23 Low 7 8 10 -Referring to Instruction 15-4,a test was conducted to determine if a relationship exists between defect rate and years of experience.Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at ? = 0.05.

Instruction 15-9 The director of admissions at a local university is interested in investigating if admissions status (admitted,waiting list,denied admission)is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to run a chi-square test of independence with a level of significance of 0.01. -Referring to Instruction 15-9,the same decision would be made with this test if the level of significance had been 0.05.

Instruction 15-11 Recent studies have found that Australian children are more obese than in the past.The amount of time children spent watching television has received much of the blame.A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television.You are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance. | TV Hours | Weights 0-3 3-6 6+ Total More than 10 kg overweight 1 9 20 30 Within 10 of normal weight 20 15 15 50 More than 10 underweight 10 5 5 20 Total 31 29 40 100 -Referring to Instruction 15-11,the degrees of freedom of the test statistic are

Instruction 15-6 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation,he found that 65 accounting majors and 52 economics majors had job offers.If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2",perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Instruction 15-6,the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Instruction 15-8 Four surgical procedures currently are used to install pacemakers.If the patient does not need to return for follow-up surgery,the operation is called a "clear" operation.A heart centre wants to compare the proportion of clear operations for the four procedures,and collects the following numbers of patients from their own records: | Procedure | Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance. -Referring to Instruction 15-8,there is sufficient evidence to conclude that the proportions between procedure C and procedure D are different at a 0.05 level of significance.